Volker Betz, Jozsef Lorinczi
A Gibbsian description of P(\phi)_1-processes
(235K, postscript)
ABSTRACT. We consider Brownian motions perturbed by suitable potentials
and ask the question whether their stationary path measures can
be described as Gibbs measures. Our main result is that for a
rich set of potentials and a large subset of boundary conditions
Gibbs measures do exist and are moreover unique. The set of
allowed boundary path configurations is identified explicitely.
We conclude by illustrating these results on some specific examples.